5 Assessment of Groundwater Quality in Sri Lanka …
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5.2.3 Statistical Analysis
Data were standardized using Z scale transformation (Nosrati and Van Den Eeckhaut
2012).
Z =
(X − x)
S
Here, X, x and S are representing unedited values of variable, mean and standard
deviation, respectively. It is necessary in multivariate cluster analysis to improve
homogeneity of data. Further, it ensures that data are in vicinity of the variance and
all the variables are weighted equally in hierarchical cluster analysis (Noshadi and
Ghafourian 2016 and Daughney et al. 2012).
Statistical analyses of the data were performed using SPSS version 16.0 (SPSS
Inc. 2004) and the Statistica version 12.
5.2.4 Cluster Analysis
Cluster analysis (CA) was performed to classify the data set into groups based on
the attributes of the objects with respect to a set of special characteristics (Noshadi
and Ghafourian 2016). Accordingly, samples having high homogeneity levels are
classified under same category, while samples having high heterogeneity levels are
classified under different categories (Juahir et al. 2011). Hierarchical agglomerative
CA was performed on the standardized data set by means of the Ward’s method,
using squared Euclidean distances as a measure of similarity.
5.2.5 Factor Analysis
Factor analysis (FA) is used to reduce the contribution of less significant variables by
simplifying the data resulting from a principal component analysis (PCA) (Nosrati
and Van Den Eeckhaut 2012). PCA was performed on the standardized data set in
order to transmute original data set into uncorrelated new variables called principal
components (PCs), which are linear combinations of the original data set. In PCA,
the eigenvalues are a measure of their associated variances (Meglen 1992). Factors
having eigenvalues >1 explain more total variance, while factors having eigenvalue
<1 explain less total variance. Therefore, PCs having eigenvalue higher than 1 were
retained, while PCs having eigenvalue less than 1 are normally neglected (Juahir
et al. 2011).
Varimax rotation was applied to the retained factors. Rotation of PCs is a simple
and a meaningful representation of the retaining factors as it decreases the contribution of the variables with minor significance to PCs and increases the more
121
5.2.3 Statistical Analysis
Data were standardized using Z scale transformation (Nosrati and Van Den Eeckhaut
2012).
Z =
(X − x)
S
Here, X, x and S are representing unedited values of variable, mean and standard
deviation, respectively. It is necessary in multivariate cluster analysis to improve
homogeneity of data. Further, it ensures that data are in vicinity of the variance and
all the variables are weighted equally in hierarchical cluster analysis (Noshadi and
Ghafourian 2016 and Daughney et al. 2012).
Statistical analyses of the data were performed using SPSS version 16.0 (SPSS
Inc. 2004) and the Statistica version 12.
5.2.4 Cluster Analysis
Cluster analysis (CA) was performed to classify the data set into groups based on
the attributes of the objects with respect to a set of special characteristics (Noshadi
and Ghafourian 2016). Accordingly, samples having high homogeneity levels are
classified under same category, while samples having high heterogeneity levels are
classified under different categories (Juahir et al. 2011). Hierarchical agglomerative
CA was performed on the standardized data set by means of the Ward’s method,
using squared Euclidean distances as a measure of similarity.
5.2.5 Factor Analysis
Factor analysis (FA) is used to reduce the contribution of less significant variables by
simplifying the data resulting from a principal component analysis (PCA) (Nosrati
and Van Den Eeckhaut 2012). PCA was performed on the standardized data set in
order to transmute original data set into uncorrelated new variables called principal
components (PCs), which are linear combinations of the original data set. In PCA,
the eigenvalues are a measure of their associated variances (Meglen 1992). Factors
having eigenvalues >1 explain more total variance, while factors having eigenvalue
<1 explain less total variance. Therefore, PCs having eigenvalue higher than 1 were
retained, while PCs having eigenvalue less than 1 are normally neglected (Juahir
et al. 2011).
Varimax rotation was applied to the retained factors. Rotation of PCs is a simple
and a meaningful representation of the retaining factors as it decreases the contribution of the variables with minor significance to PCs and increases the more